202 Lec 10

# 202 Lec 10 - SWITCHING EXAMPLELECTURE 10 DATA iin(t 2u(t 4...

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SWITCHING EXAMPLE—LECTURE 10 DATA : i in ( t ) 2 u ( t ) 4 u ( t 1) 2 u ( t 2) , i L (0 ) 0 , Switch moves to A at t = 0; Switch moves back to B at t = 1; Switch moves back to A at t = 2 and remains there. Step 1: 0 t < 1 s Equivalent circuit in s-domain: I in ( s ) 2 s and I L ( s ) 2 s 2 s 1 2 s 4 s ( s 2) 2 s 2 s 2 . Therefore i L ( t ) 2 1 e 2 t u ( t ), 0 t 1 . Step 2: 1 t < 2 s or 0 t' < 1 where t' = t – 1. Equivalent circuit in s-domain with respect to t': One observes that the current source which accounts for the IC on the inductor at t 1

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is part of the value of I L ( s ) in contrast to what Professor Ray did in class!!!!! He made the same mistake he warned you about. Nevertheless the current moving up through the resistor (from bottom to top) is I L ( s ). Thus I L ( s ) 0.5 0.5 2 s i L (1 ) s i L (1 ) s 4 Hence i L ( t ') i L (1 ) e
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